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8th Grade Final Exam Study Guide
Unit 1 – Expressions and Equations
1. Translate the following verbal expressions into algebraic expressions.
a. six subtracted from b ______
b. nine times z ______
c. seven is added to d ______
d. five less than h ______
e. sum of w and 9 ______
f. 8 divided by b ______
g. the product of -12 and r ______
h. the quotient of x and 4 ______
2. Evaluate the following expressions.
A. -2 + 8(7 – 3d); use d = 8
B. y2 – x; use x = 7 and y = 7
C. m2 + p 5; use m = 3 and p = 15
D. z(x + y); use x = 6, y = 8, and z = 6
E. p3 + 10 + m; use m = 4, and p = 3
F. ab – c; use a = -4, b = 3, and c = -2
3. Combine Like Terms
a. 3b + 4b
b. -12c + 6c – 4c
c. 5a2 – 6a + 7a2 + 3a – 2 + 8a + 7
d. 9x3 – 7x2 + 4x2 – x + 4x3 – 3x2
e. 2h2 – 7h + 2h2 – h + 6 + 4h – 9h
f. 4ab – 6ab + 3a2b + 4ab2 + 5a2b
g. 7xy – 4x2y2 + 2xy2 + 6xy +3x2y2 – 7x2y2
4. Use the distributive property to simplify each expression.
a. 5(x – 4)
b. -3(-2x +7)
c. (9m + 10)2
d. 8(-b – 4)
e. -8(-4 – 3n)
f. –(6x + 4)
g. -2(4x – 5y)
5. Simplify each expression. Remember: distribute first then combine like terms.
a. -2(7 – n) + 4
b. -8(-5b + 7) + 5b
c. -4p – (1 – 6p)
d. 4 – 5(-4n + 3)
e. -7(k – 8) + 2k
f. 1 + 7(1 – 3b)
g. 3 – 8(7 – 5n)
Solve and check the following equations.
SolveCheck
1.2. d – 5 = -3
3. 12 + c = 7
4. -6s = 42
5. 3x + 8 = 32
6. 5 + 7x = 12
7. -6x + 5 = 5
8. 1 + 7x = -6
9. 52 = 4x + 3x + 10
10. -5 + 7x + 2x = -59
11. 4 + 3x + 5x = 4
12. -6(3x + 10) = -78
13. -3(6 – 7x) = 192
14. 7(-3 + 4x) = -77
15. -4(4 + 5x) = -76
16. p – 1 = 5p + 3p – 8
17. 5n + 34 = -2(1 – 7n)
18. 2(4x – 3) – 8 = 4 + 2x
19. -18 – 6k = 6(1 + 3k)
20. 3n – 5 = -8(6 + 5n)
Solve the following equations for x.
1. 7x = t / 2.3. ax – c = b / 4. fx + 3y = 2z
Unit 2 – Ratios, Rates and Proportions
1. There are 52 animals in the field. Twenty are cows and the rest are horses.
Write the ratio in three ways:
a. The number of cows to the number of horses
b. The number of horses to the number of animals in the field
2. There are 33 cupcakes. Nine are chocolate, 14 are vanilla and the rest are strawberry. What is the ratio of vanilla cupcakes to strawberry cupcakes?
3. Tom has 13 video games. 5 are action games, 2 are adventure and the rest are sports. How many sports games to action games does Tom have?
4. Write 2 ratios that are equivalent to the following ratios.
a. 2:5
b. 10:20
c. 6:8
5. A cat breathes about 25 times each minute. A dog breathes about 20 times per minute.
What is the ratio of dog breaths to cat breaths? ______
Write an equivalent ratio for dog breaths to cat breaths. ______
6. Shelly planted 8 tomato plants and 4 pepper plants in her garden.
What is the ratio of tomato plants to pepper plants? ______
Write an equivalent ratio for tomato plants to pepper plants. ______
7. In one game, Cindy made 4 of the 6 goals for her field hockey team.
What is the ratio of Cindy’s goals to the total teams goals? ______
Write an equivalent ratio for Cindy’s goals to the total teams goals. ______
8. Are the following ratios equivalent?
a. 2:3 and 4:6
b. 9:5 and 18:15
9. Find the unit rate. Round to the nearest hundredth.
a. 7 calculators cost $120
b. $5.00 for 2 cans of tuna
c. mowed 5 yards for $15
d. 8 chocolate bars cost $19
10. Which is the better buy?
a. 3 batteries for $4.80 or 12 batteries for $14.76
b. 22 staplers for $330 or 4 staplers for $80
c. 18 pens for $6.84 or 30 pens for $8.40
d. $15.98 for 34 liters or $4.68 for 12 liters
11. Morristown is 3.027 square miles and has a population of 18,411. Find its population density. (population/square mile)
12. Mendham is 6 square miles and has a population of 4,981. Find its population density.
Solve the following proportions.
13. / 14.15. / 16.
17. / 18.
Set up a proportion to solve the following word problems.
1. If 3 apples cost $6, how much would 12 apples cost?
2.Three tea bags are needed to make a gallon of iced tea. How many tea bags are needed to make four gallons?
3.If 3 twinkies cost $1, how much is it for 15 twinkies?
4.The ratio of teachers to students needs to be 1:30. If there were 120 students, how many teachers would be needed?
5.To make lemonade, you need 6 lemons and 8 cups of water. How many lemons do you need if you have 24 cups of water?
Unit 3 – Percents
1. Change the following decimals to percents.
a. 0.34 ______
b. 1.65 ______
c. 0.3456 ______
d. 0.452 ______
e. 0.006 ______
f. 0.1 ______
g. 3.63 ______
2. Change the following percents to decimals.
a. 78% ______
b. 125% ______
c. 8% ______
d. 90% ______
e. 445% ______
f. 1% ______
g. 0.5% ______
3. Write each as a fraction in simplest form.
a. 25% ______
b. 70% ______
c. 93% ______
d. 58% ______
e. 50% ______
f. 20% ______
g. 80% ______
4. Solve the following percent problems. Round to two decimal places if necessary.
a. What percent of 54 is 42?
b. What percent of 54 is 46?
c. What is 33% of 21?
d. 55 is 50% of what?
e. What is 71% of 89?
f. What is 70% of 56?
g. 13 is 30% of what?
h. 19 is 68% of what?
i. What is 76% of 85?
j. 34 is 53% of what?
k. What percent of 134 is 67?
5. Find the percent of change. () Round to the nearest whole percent.
a. From 45 ft to 92 ft
b. From 24 grams to 96 grams
c. From $246 to $221
d. The World Future Society predicts that by the year 2020, airplanes will be able to carry 1400 passengers. Today’s biggest jets can carry 600 passengers. What
will be the percent of increase of airplane passengers?
e. As soon as a new car is purchased and driven away from the dealership, it
begins to lose its value, or depreciate. Alonso bought a 1994 Plymouth Neon for
$9559. One year later, the value of the car was $8500. What was the percent of
decrease of the value of the car?
6. A manager wants to provide a 25% discount for everything in his store. Find the sale price of a $24 sweater.
7. The manager has pants priced at $48 that he needs to mark down 35%. What will be the sale price?
8. Mark wants to purchase a stereo that is on sale for 30% off. The stereo’s original cost is $525. How much is the sale price?
9. A bracelet that is originally priced at $140, is to be marked down by 15%. What is the sale price?
10. If the restaurant bill is $42 and you want to leave a 20% tip, how much tip will you leave? How much is the total cost of the meal?
11. A car costs $24,600. If sales tax in NJ is 7%, how much sales tax will the customer pay? How much will the car cost in total?
12. What is the total cost of a $300 stereo in the state of NJ (7% sales tax)?
13. A $62 restaurant tab is put on the table. The couple plans on leaving a 18% tip. How much should be left all together?
Unit 4 – Inequalities
Directions: Draw the correct graph for the inequality.
1.
2.
Directions: Write the correct inequality that matches the graph.
3.
4.
5. . -8
6.
7.
8.
9. 2x + 4 24
10.
11. 6x + 2 + 6x < 14
12. -3 – 6(4x + 6)> -111
13. -1 – 6x – 6 > -11 – 7x
14. 3(p – 3) – 5p > -3p – 6